Let $f(x)$ be a function satisfying $f(x)+f(\pi-x)=\pi^{2}, \forall x \in \mathbb{R}$. Then $\int_\limits{0}^{\pi} f(x) \sin x d x$ is equal to :

Question

$\pi^{2}$

$\frac{\pi^{2}}{2}$

$2 \pi^{2}$

$\frac{\pi^{2}}{4}$

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